Difference between revisions of "University of South Carolina High School Math Contest/1993 Exam/Problem 20"
Michael1129 (talk | contribs) (→Solution) |
|||
Line 6: | Line 6: | ||
== Solution == | == Solution == | ||
We have <math>(1+1)(1+2)(1+3)(1+4)(1+5)(1+6)-1</math> (The <math>-1</math> since we have one less set). This is <math>7!-1=5039</math>. | We have <math>(1+1)(1+2)(1+3)(1+4)(1+5)(1+6)-1</math> (The <math>-1</math> since we have one less set). This is <math>7!-1=5039</math>. | ||
+ | If you don't understand what the above means, just think about the simplifying of the brackets. Open the brackets and you should notice why it is correct. | ||
---- | ---- |
Revision as of 11:02, 19 October 2021
Problem
Let be the 63 nonempty subsets of . For each of these sets , let denote the product of all the elements in . Then what is the value of ?
Solution
We have (The since we have one less set). This is . If you don't understand what the above means, just think about the simplifying of the brackets. Open the brackets and you should notice why it is correct.